Avon is a town in Washington Township, Hendricks County, Indiana, United States. The population was 21,474 at the 2020 census. It is part of the Indianapolis metropolitan area. The first settlement at Avon was made around 1830. The first post office at Avon opened as "Smootsdell", in 1868. It was renamed "Avon" in 1870, and remained in operation untiā¦Avon is a town in Washington Township, Hendricks County, Indiana, United States. The population was 21,474 at the 2020 census. It is part of the Indianapolis metropolitan area. The first settlement at Avon was made around 1830. The first post office at Avon opened as "Smootsdell", in 1868. It was renamed "Avon" in 1870, and remained in operation until it was discontinued in 1902. The present name comes from the River Avon in England.